Question

Q- with reference to the figure below show that the line of action the force acts at a distance yp from point O given by the relation : ab3 12 Yp = s+-+ Is+b+ Polab P2 pgsine] de dimens where wity anceerd

Answer 1

Solution: Pam= Po where, Y = centrord distance from free liquid Surface =Stb/ The = yesino Yp= centre of pressure distance from free liquid surface A = a b Jo ye The resultant Hydrostatic force FR = (PdA FR = (Po + Pgy, Sine) A The location of Line of Action is determined by equating the moment moment of the disturbed pressure to the of resultant force about the x-axis. YXFR = JYPdA = Jy (Potegy Sine da - Po Syda + Pg sine fydA Typ XFR = POYLA + Pg sine Ixxo - et of hertian Area about X-a

YpXFR = POYA + Pg sino Ixx, Area about X-onis Where EdA is the second moment of heertior A to parallel Anis theorem, Ixo - Inic & Teda on substituting equation Ip = c + & in 1, we get; Txx.c . yt Po c pgsine ] also, Ye = stb , Ixxcc = ab² , A=ab. | Yp - St b + ab Pasino the distance where the This line is the of action required of the expression for force acts.